Question

Find the HCF of 117 and 65 and express it as a linear combination of 117 & 65.

Answer 1

Step-by-step explanation:

ANSWER

Given integers are 65 and 117 such that 117>65

Applying division lemma to 65 and 117, we get

117=65×1+52

Since the remainder 52



=0. So, apply the division lemma to the divisor 65 and the remainder 52 to get

65=52×1+13

We consider the new divisor 52 and the new remainder 13 and apply division lemma, to get

52=13×4+0

At this stage the remainder is zero. So, that last divisor or the non-zero remainder at the earlier stage i.e. 13 is the HCF of 65 and 117.

From (ii), we have

13=65−52×1

⇒13=65−(117−65×1)

⇒13=65−117+65×1

⇒13=65×2+117×(−1)

⇒13=65m+117n, where m=2 and n=−1.